Participants will be individuals with sickle cell disease, age 18 to 60, who have some degree of albuminuria. A total of 19 subjects, males and females, will be enrolled. The study is made up of Screening, Treatment, and Follow Up phases and has a cross-over design. After patients are screened for eligibility, they will be randomized to receive atorvastatin or placebo in the initial six-week treatment period. When that is complete, there will be a four-week washout period before they begin another six-week treatment period. In the second treatment period, they "cross-over" to the other treatment arm. Four weeks after the end of the second treatment period, follow-up safety assessments will be done.